Question

he safety director of a large steel mill took samples at random from company records of minor work-related accidents and classified them according to the time the accident took place.

Number of | Number of | |||||||

Time | Accidents | Time | Accidents | |||||

8 up to 9 a.m. | 10 | 1 up to 2 p.m. | 6 | |||||

9 up to 10 a.m. | 6 | 2 up to 3 p.m. | 8 | |||||

10 up to 11 a.m. | 6 | 3 up to 4 p.m. | 7 | |||||

11 up to 12 p.m. | 16 | 4 up to 5 p.m. | 20 | |||||

Using the goodness-of-fit test and the 0.01 level of significance, determine whether the accidents are evenly distributed throughout the day.

*H*_{0}: The accidents are evenly distributed
throughout the day.

*H*_{1}: The accidents are not evenly distributed
throughout the day.

a) State the decision rule, using the 0.01 significance level.

b) Compute the value of chi-square.

c)What is your decision regarding *H*_{0}?

Answer #1

A)The significance level for a given hypothesis test is a value for
which a P-value less than or equal to is considered statistically
significant. If the p value is 0.01 is considered significant or
insignificant for confidence interval of 0.99.

B)

observed frequencies of accidents (fo)=10,6,6,16,6,8,7,20

Total of accidents are: 10+6+6+19+6+8+7+20=79

Average = 79/8

expected frequencies (fe)= 79/8,79/8,79/8,/79/8,79/8,79/8,79/8,79/8

H0: Accidents are evenly distributed throughout the day

H1: Accidents are not evenly distributed throughout the day

chi-square test -statistic =sum(fo-fe)^2/fe = 20.09

Critical value = chi-inv(0.01,7)= 18.475

C)

Since the test statistic does fall inside the rejection region, we
do reject H0.

Using a 0.01 level of significance there is sufficient evidence to
conclude that

the accidents are not evenly distributed throughout the day.

The safety director of large steel mill took samples at random
from company records of minor work-related accidents and classified
them according to the time the accident took place.
Number of
Number of
Time
Accidents
Time
Accidents
8 up to 9 a.m.
5
1 up to 2 p.m.
6
9 up to 10 a.m.
10
2 up to 3 p.m.
9
10 up to 11 a.m.
8
3 up to 4 p.m.
9
11 up to 12 p.m.
18
4...

The safety director of a large steel mill took samples at random
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Number of
Number of
Time
Accidents
Time
Accidents
8 up to 9 a.m.
8
1 up to 2 p.m.
8
9 up to 10 a.m.
4
2 up to 3 p.m.
10
10 up to 11 a.m.
8
3 up to 4 p.m.
9
11 up to 12 p.m.
11...

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